A well-known asymptotically continuous quantity is
the Von Neumann entropy of density matrices
\(S(\rho ) = -{\rm tr}\, \rho \log \rho \) . This asymptotic continuity is, in turn, used to show
the asymptotic continuity of many other entanglement measures.
Asymptotic continuity is often a key step in deriving expressions or
bounds for the asymptotic rates in quantum information processing
tasks, see [1]}, [2]} for examples.
